Rank-1 preserving linear maps on nest algebras

✍ Scribed by Jinchuan Hou; Jianlian Cui

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 160 KB
• Volume: 369
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(02)00725-5

✦ Synopsis

In this paper, we characterize rank-1 preserving linear maps between nest algebras acting on real or complex Banach spaces. As applications, we show that every weakly continuous and surjective local automorphism (or, anti-automorphism) on a nest algebra with an additional property is either an automorphism or an anti-automorphism; furthermore, every weakly continuous and surjective local inner automorphism on such nest algebras is in fact an inner automorphism.